Skip to main content

Part of the book series: NATO ASI Series ((NSSB,volume 237))

Abstract

The nonlinear behavior of electrohydrodynamic convection in planarly aligned nematic liquid crystals is reviewed. Based on two-dimensional, universal envelope descriptions we present new results on undulated roll structures in the vicinity of a normal-to-oblique roll transition, wavelength selection by the Eckhaus processes, dynamics and ordering of defects in travelling roll patterns (also applicable to homogeneous Hopf bifurcations), and mean-flow induced turbulence.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W. Zimmermann and L. Kramer, Phys. Rev. Lett. 55, 402 (1985).

    Article  Google Scholar 

  2. E. Bodenschatz, W. Zimmermann and L. Kramer, J. Phys. France 49, 1875 (1988).

    Article  Google Scholar 

  3. N. V. Madhusudana, V. A. Raghunathan and K. R. Sumathy, Pramana-J. Phys. 28, L 311 (1987);

    Article  Google Scholar 

  4. V. A. Raghunathan and N. V. Madhusudana, Pramana-J. Phys. 31, L 163 (1988);

    Article  Google Scholar 

  5. W. Thom, W. Zimmermann and L. Kramer, Liquid Crystals (in press).

    Google Scholar 

  6. N. V. Madhusudana and V. A. Raghunathan, Mol. Cryst. Liq. Cryst. Lett. 5, 201 (1988).

    Google Scholar 

  7. L. Kramer, E. Bodenschatz, W. Pesch, W. Thom and W. Zimmermann, submitted to Liquid Crystals.

    Google Scholar 

  8. W. Zimmermann and W. Thom, to be published.

    Google Scholar 

  9. S. Kai and K. Hirakawa, Suppl. Progr. Theor. Phys. 64, 212 (1978);

    Article  Google Scholar 

  10. S. Kai and K. Hirakawa, Mem. Fac. Engin. Kyushu Univ. 36, 269 (1977).

    Google Scholar 

  11. A. Joets and R. Ribotta, Phys. Rev. Lett. 60, 2164 (1988);

    Article  Google Scholar 

  12. I. Rehberg, S. Rasenat and V. Steinberg, preprint 1988.

    Google Scholar 

  13. A. Joets and R. Ribotta, in “Cellular Structures in Instabilities”, J. E. Wesfreid and S. Zaleski, Eds. ( Springer, Berlin ) 1984, p. 294;

    Google Scholar 

  14. R. Ribotta, A. Joets and Lin Lei, Phys. Rev. Lett. 56, 1595 (1986);

    Article  Google Scholar 

  15. A. Joets and R. Ribotta, J. Phys. France 47, 595 (1986).

    Article  Google Scholar 

  16. M. Kaiser, Diploma thesis, Bayreuth, 1988;

    Google Scholar 

  17. M. Kaiser, W. Pesch and E. Bodenschatz, to be published.

    Google Scholar 

  18. W. Pesch and L. Kramer, Z. Phys. B63, 121 (1986).

    Article  Google Scholar 

  19. L. Kramer, E. Bodenschatz, W. Pesch and W. Zimmermann, in “The Physics of Structure Formation”, W. Güttinger and G. Danglmayr, eds. ( Springer-Verlag, Heidelberg, 1987 ) p. 136.

    Chapter  Google Scholar 

  20. A. C. Newell and J. A. Whitehead, J. Fluid Mech. 38, 279 (1969);

    Article  MathSciNet  Google Scholar 

  21. L. A. Segel, J. Fluid Mech. 38, 203 (1969).

    Article  Google Scholar 

  22. S. Kai in “Noise in Nonlinear Dynamical Systems”, P.V. E. Mc Clintock and F. Moss, eds. (Cambridge University Press, 1987 );

    Google Scholar 

  23. H. Yamazaki, S. Kai and K. Hirakawa, J. Phys. Soc. Japan 56, 1 (1987).

    Article  Google Scholar 

  24. V. Steinberg, J. Feinberg, E. Moses and I. Rehberg, preprint 1988.

    Google Scholar 

  25. P. Coullet, L. Gil, and J. Lega, preprint 1988 and this conference.

    Google Scholar 

  26. See e.g. M. Abromowitz and I. Stegun, “Handbook of Mathematical Functions” (Dover, New York, 1965) Chapts. 16 and 17.

    Google Scholar 

  27. M. Lowe and J. Gollub, Phys. Rev. Lett. 55, 2575 (1985).

    Article  Google Scholar 

  28. L. Kramer and W. Zimmermann, Physica D16, 221 (1985).

    Google Scholar 

  29. E. Bodenschatz and L. Kramer, Physica D27, 249 (1987).

    Google Scholar 

  30. W.H. Zurek, Nature 317, 505 (1985).

    Article  Google Scholar 

  31. L. Kramer, H. Schober and W. Zimmermann, Physica D31, 212 (1988).

    Google Scholar 

  32. E. Bodenschatz, W. Pesch and L. Kramer, Physica D32, 135 (1988).

    Google Scholar 

  33. A.C. Newell, Lect. appl. Math. 15, 157 (1974).

    Google Scholar 

  34. J.T. Stewart and R.C. DiPrima, Proc. R. Soc. London A362, 27 (1978).

    Article  Google Scholar 

  35. W. Zimmermann, Doctoral thesis, Bayreuth, 1987.

    Google Scholar 

  36. P. Coullet and J. Lega, Europhys. Lett. 7, 511 (1988).

    Article  Google Scholar 

  37. L. Gil, J. Lega and J.L. Meunier, preprint 1988.

    Google Scholar 

  38. P.S. Hagan, SIAM J. Appl. Math, 42 762 (1982).

    Google Scholar 

  39. Y. Kuramoto “Chemical Oscillations, Waves and Turburlence” ( Springer, Berlin, 1984 ) P 106.

    Google Scholar 

  40. L. Gil and J. Lega, private communication.

    Google Scholar 

  41. S. Kai (private communication) and M. de la Torre, I. Rehberg (private communication).

    Google Scholar 

  42. See e.g. F.H. Busse,Rep.Prog.Phys., 41, 1931, (1978).

    Article  Google Scholar 

  43. E.Siggia and A.Zippelius Phys.Fluids 26,2905,(1983).

    Article  Google Scholar 

  44. F.H. Busse and E.W. Bolton J.Fluid Mech. 146, 115, (1984).

    Article  Google Scholar 

  45. A.J. Bernoff,Univ.of Arizona,Tuscon (Preprint 1986).

    Google Scholar 

  46. P.Coullet,P.Huerre and R.Yang (This conference).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Plenum Press, New York

About this chapter

Cite this chapter

Bodenschatz, E., Kaiser, M., Kramer, L., Pesch, W., Weber, A., Zimmermann, W. (1990). Patterns and Defects in Liquid Crystals. In: Coullet, P., Huerre, P. (eds) New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena. NATO ASI Series, vol 237. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-7479-4_20

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-7479-4_20

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4684-7481-7

  • Online ISBN: 978-1-4684-7479-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics